Chain rule

Problem

The following table lists the values of functions ffff and hhhh, and of their derivatives, f′f'f​′​​f, prime and h′h'h​′​​h, prime, for the xxxx-values −2-2−2minus, 2 and 4444.

xxxx

f(x)f(x)f(x)f, left parenthesis, x, right parenthesis

h(x)h(x)h(x)h, left parenthesis, x, right parenthesis

f′(x)f'(x)f​′​​(x)f, prime, left parenthesis, x, right parenthesis

h′(x)h'(x)h​′​​(x)h, prime, left parenthesis, x, right parenthesis

−2-2−2minus, 2

12121212

−7-7−7minus, 7

28282828

−11-11−11minus, 11

4444

6666

−2-2−2minus, 2

5555

1111

Let function HHHH be defined as H(x)=f(h(x))H(x)=f\Bigl(h(x)\Bigr)H(x)=f(h(x))H, left parenthesis, x, right parenthesis, equals, f, left parenthesis, h, left parenthesis, x, right parenthesis, right parenthesis.